Ответ:

Cos5x+cos7x=cos(π+6x)

2cos6xcosx=-cos6x

2cos6xcosx+cos6x=0

cos6x(2cosx+1)=0

cos6x=0  x=П/12+Пk/6

cosx=-1/2   x=П+-П/3+2Пk

                   x=+-2/3П+2Пk